Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. G. Ramesh
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 51
NPTEL Course Size : 4.5 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Semi Inner product spaces
Lecture 2 - Inner Product Spaces
Lecture 3 - Parallelogram law
Lecture 4 - Hilbert Spaces
Lecture 5 - Orthogonality
Lecture 6 - Projection Theorem
Lecture 7 - Linear Operator
Lecture 8 - Bounded Operators
Lecture 9 - Norm of a linear operator
Lecture 10 - Examples of bounded operators
Lecture 11 - The Adjoint Operator
Lecture 12 - The Adjoint: Properties
Lecture 13 - Closed range operators - 1
Lecture 14 - Closed range operators - 2
Lecture 15 - Self-adjoint Operators
Lecture 16 - Normal operators
Lecture 17 - Isometris and Unitaries
Lecture 18 - Isometris and Unitaries
Lecture 19 - Mutually Orthogonal Projections
Lecture 20 - Invariant Subspaces
Lecture 21 - Monotone Convergence Theorem
Lecture 22 - Square root
Lecture 23 - Polar decomposition
Lecture 24 - Invertibility
Lecture 25 - Spectrum
Lecture 26 - Spectral Mapping Theorem
Lecture 27 - The spectral radius formula
Lecture 28 - multiplicative linear functionals
Lecture 29 - The GKZ-theorem
Lecture 30 - Maximal Ideal Space
Lecture 31 - Commutative C*-algebras
Lecture 32 - Decomposition of spectrum
Lecture 33 - Computing spectrum: Examples
Lecture 34 - Approximate spectrum
Lecture 35 - Approximate spectrum: Properties
Lecture 36 - Numerical bounds
Lecture 37 - Compact Operators
Lecture 38 - Compact Operators; Properties
Lecture 39 - Spectral Theorem: Compact Self-Adjoint Operators
Lecture 40 - Spectral Theorem: Consequences
Lecture 41 - Compact Normal Operators
Lecture 42 - Compact Operators Singular value Decomposition
Lecture 43 - Fredholm Alternative Theorem
Lecture 44 - Orthogonal decomposition of self-adjoint operators
Lecture 45 - Spectral family; Properties - I
Lecture 46 - Spectral family; Properties - II
Lecture 47 - Spectral theorem Self adjoint Operators
Lecture 48 - Spectral theorem Examples
Lecture 49 - Spectral theorem: Consequences
Lecture 50 - Continuous functional Calculus
Lecture 51 - Spectral mapping theorem